Analysis of 111/999 NHS calls and 111 online reports
Quentin Leclerc, Emily Nightingale, Samuel Abbott & Thibaut Jombart, for CMMID
Wednesday 06 January 2021
1 Data preparation
1.1 Outline
Load scripts: loads libraries and useful scripts used in the analyses; all
.Rfiles contained inscriptsat the root of the factory are automatically loadedLoad data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.
1.2 Load packages
library(reportfactory)
library(here)
library(rio)
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)1.3 Load scripts
These scripts will load:
- all scripts stored as
.Rfiles inside/scripts/ - all scripts stored as
.Rfiles inside/src/
These scripts also contain routines to access the latest clean encrypted data (see next section).
1.4 Load clean data
We import the latest NHS pathways data:
x <- import_pathways() %>%
as_tibble()
x
## [90m# A tibble: 391,248 x 11[39m
## site_type date sex age ccg_code ccg_name count postcode nhs_region
## [3m[90m<chr>[39m[23m [3m[90m<date>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<int>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m
## [90m 1[39m 111 2020-03-18 fema… miss… e380000… nhs_glo… 1 gl34fe South West
## [90m 2[39m 111 2020-03-18 fema… miss… e380001… nhs_sou… 1 ne325nn North Eas…
## [90m 3[39m 111 2020-03-18 fema… 0-18 e380000… nhs_air… 8 bd57jr North Eas…
## [90m 4[39m 111 2020-03-18 fema… 0-18 e380000… nhs_ash… 7 tn254ab South East
## [90m 5[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bar… 35 rm13ae London
## [90m 6[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bar… 9 n111np London
## [90m 7[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bar… 11 s752py North Eas…
## [90m 8[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bas… 19 ss143hg East of E…
## [90m 9[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bas… 6 dn227xf North Eas…
## [90m10[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bat… 9 ba25rp South West
## [90m# … with 391,238 more rows, and 2 more variables: day [3m[90m<int>[90m[23m, weekday [3m[90m<fct>[90m[23m[39mWe also import demographics data for NHS regions in England, used later in our analysis:
path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
## nhs_region variable value
## 1 North West 0-18 0.22538599
## 2 North East and Yorkshire 0-18 0.21876449
## 3 Midlands 0-18 0.22564656
## 4 East of England 0-18 0.22810783
## 5 London 0-18 0.23764782
## 6 South East 0-18 0.22458811
## 7 South West 0-18 0.20799797
## 8 North West 19-69 0.64274078
## 9 North East and Yorkshire 19-69 0.64437753
## 10 Midlands 19-69 0.63876675
## 11 East of England 19-69 0.63034229
## 12 London 19-69 0.67820084
## 13 South East 19-69 0.63267336
## 14 South West 19-69 0.63176131
## 15 North West 70-120 0.13187323
## 16 North East and Yorkshire 70-120 0.13685797
## 17 Midlands 70-120 0.13558669
## 18 East of England 70-120 0.14154988
## 19 London 70-120 0.08415135
## 20 South East 70-120 0.14273853
## 21 South West 70-120 0.16024072Finally, we import publically available deaths per NHS region:
dth <- import_deaths() %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
#truncation to account for reporting delay
delay_max <- 21
dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
## date_report nhs_region deaths
## 1 2020-03-01 East of England 0
## 2 2020-03-02 East of England 1
## 3 2020-03-03 East of England 0
## 4 2020-03-04 East of England 0
## 5 2020-03-05 East of England 0
## 6 2020-03-06 East of England 1
## 7 2020-03-07 East of England 0
## 8 2020-03-08 East of England 0
## 9 2020-03-09 East of England 1
## 10 2020-03-10 East of England 0
## 11 2020-03-11 East of England 0
## 12 2020-03-12 East of England 0
## 13 2020-03-13 East of England 1
## 14 2020-03-14 East of England 2
## 15 2020-03-15 East of England 2
## 16 2020-03-16 East of England 1
## 17 2020-03-17 East of England 1
## 18 2020-03-18 East of England 5
## 19 2020-03-19 East of England 4
## 20 2020-03-20 East of England 2
## 21 2020-03-21 East of England 11
## 22 2020-03-22 East of England 12
## 23 2020-03-23 East of England 11
## 24 2020-03-24 East of England 19
## 25 2020-03-25 East of England 26
## 26 2020-03-26 East of England 36
## 27 2020-03-27 East of England 38
## 28 2020-03-28 East of England 28
## 29 2020-03-29 East of England 43
## 30 2020-03-30 East of England 45
## 31 2020-03-31 East of England 70
## 32 2020-04-01 East of England 62
## 33 2020-04-02 East of England 65
## 34 2020-04-03 East of England 80
## 35 2020-04-04 East of England 71
## 36 2020-04-05 East of England 76
## 37 2020-04-06 East of England 71
## 38 2020-04-07 East of England 93
## 39 2020-04-08 East of England 111
## 40 2020-04-09 East of England 87
## 41 2020-04-10 East of England 74
## 42 2020-04-11 East of England 92
## 43 2020-04-12 East of England 100
## 44 2020-04-13 East of England 78
## 45 2020-04-14 East of England 61
## 46 2020-04-15 East of England 82
## 47 2020-04-16 East of England 74
## 48 2020-04-17 East of England 86
## 49 2020-04-18 East of England 64
## 50 2020-04-19 East of England 67
## 51 2020-04-20 East of England 67
## 52 2020-04-21 East of England 75
## 53 2020-04-22 East of England 67
## 54 2020-04-23 East of England 49
## 55 2020-04-24 East of England 66
## 56 2020-04-25 East of England 54
## 57 2020-04-26 East of England 48
## 58 2020-04-27 East of England 46
## 59 2020-04-28 East of England 58
## 60 2020-04-29 East of England 32
## 61 2020-04-30 East of England 45
## 62 2020-05-01 East of England 49
## 63 2020-05-02 East of England 29
## 64 2020-05-03 East of England 41
## 65 2020-05-04 East of England 19
## 66 2020-05-05 East of England 36
## 67 2020-05-06 East of England 31
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## 75 2020-05-14 East of England 26
## 76 2020-05-15 East of England 19
## 77 2020-05-16 East of England 26
## 78 2020-05-17 East of England 17
## 79 2020-05-18 East of England 25
## 80 2020-05-19 East of England 15
## 81 2020-05-20 East of England 26
## 82 2020-05-21 East of England 21
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## 84 2020-05-23 East of England 12
## 85 2020-05-24 East of England 17
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## 136 2020-07-14 East of England 2
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## 139 2020-07-17 East of England 0
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## 142 2020-07-20 East of England 1
## 143 2020-07-21 East of England 1
## 144 2020-07-22 East of England 2
## 145 2020-07-23 East of England 1
## 146 2020-07-24 East of England 1
## 147 2020-07-25 East of England 0
## 148 2020-07-26 East of England 1
## 149 2020-07-27 East of England 1
## 150 2020-07-28 East of England 2
## 151 2020-07-29 East of England 0
## 152 2020-07-30 East of England 0
## 153 2020-07-31 East of England 1
## 154 2020-08-01 East of England 0
## 155 2020-08-02 East of England 0
## 156 2020-08-03 East of England 0
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## 243 2020-10-29 East of England 10
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## 247 2020-11-02 East of England 9
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## 249 2020-11-04 East of England 11
## 250 2020-11-05 East of England 11
## 251 2020-11-06 East of England 18
## 252 2020-11-07 East of England 10
## 253 2020-11-08 East of England 13
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## 255 2020-11-10 East of England 26
## 256 2020-11-11 East of England 14
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## 1861 2020-03-01 South West 0
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## 1872 2020-03-12 South West 0
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## 1961 2020-06-09 South West 0
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## 1966 2020-06-14 South West 0
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## 1977 2020-06-25 South West 0
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## 1979 2020-06-27 South West 0
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## 1991 2020-07-09 South West 0
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## 1993 2020-07-11 South West 0
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## 1996 2020-07-14 South West 0
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## 2010 2020-07-28 South West 0
## 2011 2020-07-29 South West 0
## 2012 2020-07-30 South West 1
## 2013 2020-07-31 South West 0
## 2014 2020-08-01 South West 0
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## 2017 2020-08-04 South West 0
## 2018 2020-08-05 South West 0
## 2019 2020-08-06 South West 0
## 2020 2020-08-07 South West 0
## 2021 2020-08-08 South West 0
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## 2024 2020-08-11 South West 0
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## 2027 2020-08-14 South West 1
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## 2164 2020-12-29 South West 18
## 2165 2020-12-30 South West 11
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## 2167 2021-01-01 South West 24
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## 2169 2021-01-03 South West 13
## 2170 2021-01-04 South West 71.5 Completion date
We extract the completion date from the NHS Pathways file timestamp:
The completion date of the NHS Pathways data is Tuesday 05 Jan 2021.
1.6 Auxiliary functions
These are functions which will be used further in the analyses.
Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:
## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here
Rsq <- function(x) {
1 - (x$deviance / x$null.deviance)
}Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:
## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals
get_r <- function(model) {
## extract coefficients and conf int
out <- data.frame(r = coef(model)) %>%
rownames_to_column("var") %>%
cbind(confint(model)) %>%
filter(!grepl("day_of_week", var)) %>%
filter(grepl("day", var)) %>%
rename(lower_95 = "2.5 %",
upper_95 = "97.5 %") %>%
mutate(var = sub("day:", "", var))
## reconstruct values: intercept + region-coefficient
for (i in 2:nrow(out)) {
out[i, -1] <- out[1, -1] + out[i, -1]
}
## find the name of the intercept, restore regions names
out <- out %>%
mutate(nhs_region = model$xlevels$nhs_region) %>%
select(nhs_region, everything(), -var)
## find halving times
halving <- log(0.5) / out[,-1] %>%
rename(halving_t = r,
halving_t_lower_95 = lower_95,
halving_t_upper_95 = upper_95)
## set halving times with exclusion intervals to NA
no_halving <- out$lower_95 < 0 & out$upper_95 > 0
halving[no_halving, ] <- NA_real_
## return all data
cbind(out, halving)
}Functions used in the correlation analysis between NHS Pathways reports and deaths:
## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.
getcor <- function(x, ndx) {
return(cor(x$deaths[ndx],
x$note_lag[ndx],
use = "complete.obs",
method = "pearson"))
}
## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)
getboot <- function(x) {
result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000),
type = "bca")
return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
r = result$t0,
r_low = result$bca[4],
r_hi = result$bca[5]))
}Function to classify the day of the week into weekend, Monday, and the rest:
## Fn to add day of week
day_of_week <- function(df) {
df %>%
dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>%
dplyr::mutate(day_of_week = dplyr::case_when(
day_of_week %in% c("Sat", "Sun") ~ "weekend",
day_of_week %in% c("Mon") ~ "monday",
!(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
) %>%
factor(levels = c("rest_of_week", "monday", "weekend")))
}Custom color palettes, color scales, and vectors of colors:
2 Temporal trends in NHS Pathways reports
2.1 Outline
We look for temporal patterns in COVID-19 related 111/999 calls and 111 online reports. Analyses are broken down by NHS region. We also look for estimates of recent growth rate and associated doubling / halving time.
2.2 Reports by region over time
tab_date_region_all <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
dth %>%
mutate(trusted = case_when(date_report < max(dth$date_report)-delay_max ~ "Y",
date_report >= max(dth$date_report)-delay_max ~ "N"),
value = "Deaths",
vline = max(dth$date_report)-delay_max-1,
lab = "Truncated for reporting delay",
lab_pos_x = vline + 10,
lab_pos_y = 150,
lab_col = "darkgrey") %>%
rename(date = date_report,
n = deaths) %>%
bind_rows(
mutate(tab_date_region_all, value = "Reports",
trusted = "Y",
vline = as.Date("2020-03-23"),
lab = "Start of UK lockdown",
lab_pos_x = vline - 8,
lab_pos_y = 30200,
lab_col = "black")
) %>%
mutate(value = factor(value, levels = c("Reports","Deaths"))) -> dths_reports
plot_dth_report <-
ggplot(dths_reports, aes(date, n, colour = nhs_region)) +
# Add main points and lines, coloured by region and fade out deaths for excluded period
geom_point(aes(alpha = trusted)) +
geom_line(alpha = 0.2) +
geom_smooth(method = "loess", span = .5, color = "black") +
scale_colour_manual("", values = pal) +
scale_alpha_manual(values = c(0.3,1)) +
guides(alpha = F) +
# Add vertical markers for important dates with labels - different for each facet
ggnewscale::new_scale_colour() +
geom_vline(aes(xintercept = vline, col = value), lty = "solid") +
geom_text(aes(x = lab_pos_x, y = lab_pos_y, label = lab, col = value), size = 3) +
scale_colour_manual("",values = c("black","darkgrey"), guide = F) +
# Facet by deaths and reports
facet_grid(rows = vars(value), scales = "free_y", switch = "y") +
# Other formatting
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",strip.placement = "outside") +
rotate_x +
labs(x = NULL,
y = NULL)
plot_dth_report
2.3 Reports by region by age over time
We plot the number of 111/999 calls and 111 online reports by age, and the proportion of 111/999 calls and 111 online reports by age. In the second graph, the vertical lines indicate the proportion of individuals residing in the corresponding NHS region who belong to the corresponding age group.
tab_date_region_age_all <- x %>%
filter(!is.na(nhs_region),
age != "missing") %>%
group_by(date, nhs_region, age) %>%
summarise(n = sum(count))
tab_date_region_age_all %>%
ggplot(aes(x = date, y = n, fill = age)) +
geom_col(position = "stack") +
scale_fill_manual(values = age.pal) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(fill = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Total daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
tab_date_region_age_all <- tab_date_region_age_all %>%
group_by(date, nhs_region) %>%
summarise(tot = sum(n)) %>%
left_join(tab_date_region_age_all, by = c("date", "nhs_region")) %>%
mutate(prop_n = n/tot)
tab_date_region_age_all %>%
ggplot(aes(x = date, y = prop_n, color = age)) +
scale_color_manual(values = age.pal) +
geom_line() +
geom_point() +
geom_hline(data = nhs_region_pop, aes(yintercept = value, color = variable)) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(color = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Proportion of daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
2.4 Moving window model
We fit quasi-Poisson GLMs for 14-day windows to get growth rates over time.
## set moving time window (1/2/3 weeks)
w <- 14
# create empty df
r_all_sliding <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding <- bind_rows(r_all_sliding, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding <- r_all_sliding %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))We examine the evolution of the growth rate by region over time.
# plot
plot_growth <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)From the growth rate, we derive R and examine its value through time.
# plot
plot_R <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
rotate_x +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
# strip.text.x = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "",
override.aes = list(fill = NA)),
fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))
2.5 Moving window model - stratified by age
We repeat the above analysis, where we fit quasi-Poisson GLMs for 14-day windows to get growth rates over time, but apply this to each age group separately (0-18, 19-69, 70-120 years old).
We first run the analysis for 0-18 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_0_18 <- NULL
## make data for model
x_model_all_moving_0_18 <- x %>%
filter(!is.na(nhs_region),
age == "0-18") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_0_18$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_0_18 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_0_18 <- bind_rows(r_all_sliding_0_18, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_0_18 <- r_all_sliding_0_18 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_0_18 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_0_18 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_0_18 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then, we run the analysis for 19-69 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_19_69 <- NULL
## make data for model
x_model_all_moving_19_69 <- x %>%
filter(!is.na(nhs_region),
age == "19-69") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_19_69$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_19_69 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_19_69 <- bind_rows(r_all_sliding_19_69, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_19_69 <- r_all_sliding_19_69 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_19_69 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_19_69 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_19_69 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Finally, we run the analysis for 70-120 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_70_120 <- NULL
## make data for model
x_model_all_moving_70_120 <- x %>%
filter(!is.na(nhs_region),
age == "70-120") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_70_120$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_70_120 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_70_120 <- bind_rows(r_all_sliding_70_120, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_70_120 <- r_all_sliding_70_120 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_70_120 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_70_120 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_70_120 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)"))) We combine the estimated growth rates and effective reproduction numbers into a single figure.
ggpubr::ggarrange(fig2_3_0_18,
fig2_3_19_69,
fig2_3_70_120,
nrow = 3,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom",
align = "hv") 
3 Comparison with deaths time series
3.1 Outline
We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.
Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.
3.2 Lagged correlation
We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.
First we join the NHS Pathways and death data, and aggregate over all England:
## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max
dth_trunc <- dth %>%
rename(date = date_report) %>%
filter(date <= trunc_date)
## join with notification data
all_data <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(count = sum(count, na.rm = T)) %>%
ungroup %>%
inner_join(dth_trunc,
by = c("date","nhs_region"))
all_tot <- all_data %>%
group_by(date) %>%
summarise(count = sum(count, na.rm = TRUE),
deaths = sum(deaths, na.rm = TRUE)) We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:
## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
## lag reports
summary <- all_tot %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI
getboot(.) %>%
mutate(lag = i)
lag_cor <- bind_rows(lag_cor, summary)
}
cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
theme_bw() +
geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_point() +
geom_line() +
labs(x = "Lag between NHS pathways and death data (days)",
y = "Pearson's correlation") +
large_txt
cor_vs_lag
This analysis suggests that the best lag is 16 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 16 days.
all_tot <- all_tot %>%
rename(date_death = date) %>%
mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
date_note = lag(date_death,16))
lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")
summary(lag_mod)
##
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -16.361 -11.253 -4.314 8.074 18.785
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.561e+00 6.581e-02 69.31 <2e-16 ***
## note_lag 1.659e-05 9.047e-07 18.34 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for quasipoisson family taken to be 98.94205)
##
## Null deviance: 50028 on 255 degrees of freedom
## Residual deviance: 26208 on 254 degrees of freedom
## (16 observations deleted due to missingness)
## AIC: NA
##
## Number of Fisher Scoring iterations: 5
exp(coefficients(lag_mod))
## (Intercept) note_lag
## 95.654167 1.000017
exp(confint(lag_mod))
## 2.5 % 97.5 %
## (Intercept) 83.876529 108.569373
## note_lag 1.000015 1.000018
Rsq(lag_mod)
## [1] 0.4761226
mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])
all_tot_pred <-
all_tot %>%
filter(!is.na(note_lag)) %>%
mutate(pred = mod_fit$fit,
pred.se = mod_fit$se.fit,
low = exp(pred - 1.96*pred.se),
hi = exp(pred + 1.96*pred.se))
glm_fit <- all_tot_pred %>%
filter(!is.na(note_lag)) %>%
ggplot(aes(x = note_lag, y = deaths)) +
geom_point() +
geom_line(aes(y = exp(pred))) +
geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
theme_bw() +
labs(y = "Daily number of\ndeaths reported",
x = "Daily number of NHS Pathways reports") +
large_txt
glm_fit
4 Supplementary figures
4.1 Serial interval distribution
This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.
SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
meanlog = log(4.7),
sdlog = log(2.9), w = 0.5)
SI_dist1 <- data.frame(x = SI_distribution$r(1e5))
SI_dist1 <- count(SI_dist1, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 30, 5)) +
theme_bw()
SI_dist2 <- data.frame(x = SI_distribution2$r(1e5))
SI_dist2 <- count(SI_dist2, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
theme_bw()
ggpubr::ggarrange(SI_dist1,
SI_dist2,
nrow = 1,
labels = "AUTO") 
4.2 Sensitivity analysis - 7 or 21 days moving window
We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.
First with the 7 days window:
## set moving time window (1/2/3 weeks)
w <- 7
# create empty df
r_all_sliding_7days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)plot_R <- r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_7days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_7days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_7 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then with the 21 days window:
## set moving time window (1/2/3 weeks)
w <- 21
# create empty df
r_all_sliding_21days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_21days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_21days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_21 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))And we combine both outputs into a single plot:
ggpubr::ggarrange(r_R_7,
r_R_21,
nrow = 2,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom") 
4.3 Correlation between NHS Pathways reports and deaths by NHS region
lag_cor_reg <- data.frame()
for (i in 0:30) {
summary <-
all_data %>%
group_by(nhs_region) %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI for each region
group_modify(~getboot(.x)) %>%
mutate(lag = i)
lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}
cor_vs_lag_reg <-
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
geom_point() +
geom_line() +
facet_wrap(~nhs_region) +
scale_color_manual(values = pal) +
scale_fill_manual(values = pal, guide = F) +
theme_bw() +
labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
theme(legend.position = "bottom") +
guides(color = guide_legend(override.aes = list(fill = NA)))
cor_vs_lag_reg
5 Export data
We save the tables created during our analysis:
if (!dir.exists("excel_tables")) {
dir.create("excel_tables")
}
## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")
for (e in tables_to_export) {
rio::export(get(e),
file.path("excel_tables",
paste0(e, ".xlsx")))
}
## also export result from regression on lagged data
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))6 System information
6.1 Outline
The following information documents the system on which the document was compiled.
6.2 System
This provides information on the operating system.
Sys.info()
## sysname
## "Darwin"
## release
## "19.6.0"
## version
## "Darwin Kernel Version 19.6.0: Thu Oct 29 22:56:45 PDT 2020; root:xnu-6153.141.2.2~1/RELEASE_X86_64"
## nodename
## "Mac-1609930367075.local"
## machine
## "x86_64"
## login
## "root"
## user
## "runner"
## effective_user
## "runner"6.3 R environment
This provides information on the version of R used:
6.4 R packages
This provides information on the packages used:
sessionInfo()
## R version 4.0.3 (2020-10-10)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.7
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] ggnewscale_0.4.4 ggpubr_0.4.0 lubridate_1.7.9.2
## [4] chngpt_2020.10-12 cyphr_1.1.0 DT_0.16
## [7] kableExtra_1.3.1 janitor_2.1.0 remotes_2.2.0
## [10] projections_0.5.2 earlyR_0.0.5 epitrix_0.2.2
## [13] distcrete_1.0.3 incidence_1.7.3 rio_0.5.16
## [16] reshape2_1.4.4 rvest_0.3.6 xml2_1.3.2
## [19] linelist_0.0.40.9000 forcats_0.5.0 stringr_1.4.0
## [22] dplyr_1.0.2 purrr_0.3.4 readr_1.4.0
## [25] tidyr_1.1.2 tibble_3.0.4 ggplot2_3.3.3
## [28] tidyverse_1.3.0 here_1.0.1 reportfactory_0.0.5
##
## loaded via a namespace (and not attached):
## [1] minqa_1.2.4 colorspace_2.0-0 selectr_0.4-2 ggsignif_0.6.0
## [5] ellipsis_0.3.1 rprojroot_2.0.2 snakecase_0.11.0 fs_1.5.0
## [9] rstudioapi_0.13 farver_2.0.3 fansi_0.4.1 splines_4.0.3
## [13] knitr_1.30 jsonlite_1.7.2 nloptr_1.2.2.2 broom_0.7.3
## [17] dbplyr_2.0.0 compiler_4.0.3 httr_1.4.2 backports_1.2.1
## [21] assertthat_0.2.1 Matrix_1.2-18 cli_2.2.0 htmltools_0.5.0
## [25] tools_4.0.3 gtable_0.3.0 glue_1.4.2 Rcpp_1.0.5
## [29] carData_3.0-4 cellranger_1.1.0 vctrs_0.3.6 nlme_3.1-149
## [33] matchmaker_0.1.1 crosstalk_1.1.0.1 xfun_0.19 ps_1.5.0
## [37] openxlsx_4.2.3 lme4_1.1-26 lifecycle_0.2.0 statmod_1.4.35
## [41] rstatix_0.6.0 MASS_7.3-53 scales_1.1.1 hms_0.5.3
## [45] parallel_4.0.3 sodium_1.1 yaml_2.2.1 curl_4.3
## [49] gridExtra_2.3 stringi_1.5.3 kyotil_2020.10-12 boot_1.3-25
## [53] zip_2.1.1 rlang_0.4.10 pkgconfig_2.0.3 evaluate_0.14
## [57] lattice_0.20-41 labeling_0.4.2 htmlwidgets_1.5.3 cowplot_1.1.1
## [61] tidyselect_1.1.0 plyr_1.8.6 magrittr_2.0.1 R6_2.5.0
## [65] generics_0.1.0 DBI_1.1.0 pillar_1.4.7 haven_2.3.1
## [69] foreign_0.8-80 withr_2.3.0 mgcv_1.8-33 survival_3.2-7
## [73] abind_1.4-5 modelr_0.1.8 crayon_1.3.4 car_3.0-10
## [77] utf8_1.1.4 rmarkdown_2.6 viridis_0.5.1 grid_4.0.3
## [81] readxl_1.3.1 data.table_1.13.6 reprex_0.3.0 digest_0.6.27
## [85] webshot_0.5.2 munsell_0.5.0 viridisLite_0.3.0